Adjustable speed drive with active filtering capability for harmonic current compensation

0 Two methods of harmonic current identification are studied: direct identification by decomposition of the current, and identification by Fourier series.. Two methods to compensate the

Adjustable Speed Drive with Active Filtering Capability for

*

Harmonic Current Compensation

Flemming Abrahamsen*, Alain David**

BORG University, Dept of Electrical Energy Conversion, Pontoppidanstraede 10 1, DK-92 Aalborg East Denmark

** ELECTRICITE DE FRANCE, R&D Division, Electrical Machines Branch, 1 av GBndral De Gaulle, 92141 Clamart France

Abstract - A new solution is proposed to solve the

problem with harmonic current pollution using diode

rectified Adjustable Speed Drives (ASD) in the mean

power range A fully controlled voltage source ASD acts

as an active filter on the network side, being able to

compensate harmonics of several conventional ASDs o r

other loads in parallel Current harmonic identification

strategies, control aspects and the limit of harmonic

current compensation are studied Simulations verified by

experimentation show excellent results This new solution

is economic compared to previous proposed filtering

techniques in ASD applications

I INTRODUCTION Recent developments in power electronics technology

have led to a significant market penetration of Adjustable

Speed Drives (ASDs), which are economical, reliable, highly

flexible, with furthermore energy savings capability

However, such equipments inject non-sinusoidal currents into

the electrical supply network of the plant and the utility

system, which is one of the major concems in the use of

ASDs The effects of these harmonic currents on both the

power system and all other electrical equipments can be

critical with possibility of overheating (typically for

transformers, electric motors, capacitors, ) or instantaneous

failures, typically for low power electronic equipments

Some Electromagnetical Compatibility (EMC) standards

must be considered, especially for limits of harmonic current

emission, typically with the IEEE-519 for the USA, and the

IEC 1000-3-2 and 1000-3-4 for most other countries and

especially for Europe If these standards are only applied as a

recommendation on industrial plants, it will be permitted to

use certain polluting equipments, but some solutions will

have to be used so that a satisfactory EMC level is obtained

between polluting equipment and polluted ones, and the plant

respects the harmonic current emission at the connection to

the public network These solutions can be as follows:

0 A good design of the intemal plant network

0 The use of passive filters For this solution, which is

presently the most common one, a preliminary electrical

network analysis is required to properly design the filter

and to avoid any resonant frequency The cost of this

design plus the price of the filter itself, which can become

0-7803-2730-6/95 $4.00 0 1995 IEEE

very large and therefore bulky, make this solution expensive

The use of non-polluting equipment with sinusoidal input currents For single-phase structures (typically up to 4

kW), there are the "diode bridge with boost-converter" [l], which is well-known and already industrially used with an extra cost of 10-15 %, or the structure "3 branches with common capacitive point" [2] Three-phase structures exist, but with an extra cost estimated to 40-50

% The structures are the "diode bridge with boost- converter" [3], or the "ASD with a hlly controlled PWM rectifier" 141

The use of active filters [ 5 ] , [ 6 ] , [7] It is one of the most

promising solutions to compensate an amount of equipment, a complete installation or a part of an electrical network This is a competitor to the solution proposed in this paper

The use of mixed equipment (Fig 1.) with an active filtering capability directly integrated in the equipment itself to compensate harmonic pollution of other conventional, and therefore polluting converters

1''' AA

Fig 1 The proposed structure of a "clean" installation of adjustable speed drives One ASD - active filter compensates the harmonics of its neighbour ASDs (with or without common dc-link) The network

current is sinusoidal

This mixed solution is described and analysed in this

paper, such as an ASD - active filter compensates harmonic pollution of 2 to 5 conventional polluting ASDs of same power rating, as illustrated in Fig 1, typically from few 10

kW to several hundreds kW power range This paper focuses

on the control system analysis of this ASD - active filter (as described in Fig 2.), and the following points are developed:

1137

0 Two methods of harmonic current identification are

studied: direct identification by decomposition of the

current, and identification by Fourier series

0 Four phase current controllers (PI, PID, pole-placement

and deadbeat) are compared

Two methods to compensate the error of the current

controllers are analyzed: compensation by phase shift and

amplification of the individual current harmonics, and

compensation by prediction of the current references

This finally leads on two viable global control systems which

are analysed and compared both on simulations and

experiments with excellent performance

The network is considered symmetrical and balanced

Only a diode-bridge, which is the most common rectifier-

type in the mean-power range, is considered as a non-linear

load The space vector modulation is used for the PWM

control with a switching frequency of 5 kHz Furthermore,

the machine is controlled in open loop with a simple control

law of constant Vlf

harmonic

identifi- control

I

1 satibn 1

.-

fundamental 1 current reference

I

I

Fig 2 Diagram for the control of the rectifier - active filter The

diagram of the inverter - motor control is not shown

11 MODELLING THE CONVERTER - ACTIVE FILTER

The modelling of a fully controlled voltage source

rectifier has already been treated by several authors [8], [9],

and is only repeated briefly here

A Model of the converter

The structure of the converter - active filter studied in this

paper is shown in Fig 3 with its non-linear load By

equalling its inverter and motor with a pure resistance, the

model of the converter - active filter in Fig 4 is obtained

load

load

Fig 3 The ASD - active filter above compensates the harmonics of the conventional ASD below The inverters are equalled with pure

resistances

'd

Fig 4 Three phase time domain model of the converter - active filter

c,, c, and cc are the control logics of the switches, p is the

differential operator and Ct32 is the transposed matrix of C32,

see (1)

r

- -

The transformation of the three-phase model of Fig 3 into a two-phase model in the rotating DQ reference frame through the matrices (1) and (2) gives:

(3 )

It is remarked that two cross-coupling terms deterniined by the angular velocity aDp of the DQ reference fi-ame are introduced in these equations

B Cascade regulation

The converter is controlled according to the principle of cascade regulation: a slow external loop controls the dc-link

voltage vd, and two intemal fast loops control the rectifier -

active filter phase currents in the DQ reference frame The

internal and extemal systems are assumed to be independent

The external system is described by the following Is' order

linear equation:

The active power P and the reactive power Q consumed by

the ASD - active filter are:

be represented by:

m

i ( t ) = z[an cos(noft) + bn s i n ( n o / t ) ] (8)

where is the fundamental angular velocity With a numerical implementation of a moving Fourier series, the coefficients become:

n=I

k

(9)

2

a n ( k ) = - C i ( j c o s ( n o f j q )

b n ( k ) = - z i ( j q ) s i n ( n o f j q ) (10)

k

N f m r j = k - ( N h r - l )

where T, is the sampling period, and Nfur an integer Or recursively:

(1 1)

By inversion of (5), and by setting P = PWJ = vdWf iZmf and

Q = QRf = 0 , where vdm/ is the dc-link reference voltage and

ilrer is the controller output of the extemal loop (see Fig 2),

the current references are calculated as follow:

an( k , = -I)

bn( k ) = bn( k - I) + - - L [ i ( k T , ) + i ( ( k N f a r - Nfour)T,)]cos(nw/kT,)

+ L [ i ( kT,) + i( ( k - Nfour) T,)] sin( n o f kT,) (12)

Nfour

[ r c ~ R / ] =

In view of making the converter work as an active filter

as well, harmonic current references are added to the

fundamental current references, calculated by (6), in each

axis (see Fig 2) The calculation of these harmonic current

references is given in section V

individual current harmonics can be identified

B Direct identflcation by decomposition ofthe current

The harmonic currents in the stationary two axis ap reference frame are calculated as follow:

-

VnetuP - Vnerp4

< V n e t p F + Vnetuq

The network voltages and cross coupling terms appearing in ilouda-h = iloadu - iloadn- f = hoada - 2 2 (13)

- (3) are compensated as shown in Fig 5

"netu +"ne@

and i,ouhy ilouder are the fundamental current components, j7 and 4 are the dc values of p and q, p is the instantaneous

active power and q is the instantaneous reactive power:

Fig 5 Compensation of network voltages and cross-coupling terms of

the internal loops p = vuiu + vpip (15)

q = -vpia + v U P i

Assuming a perfect compensation of the cross-coupling and -

-the network voltages, -the equations describing -the intemal

loops are:

The dc values of p and q are obtained by low pass filtering

using a numerical window function:

k

(17)

v @ D = ( & / + P 4 & D 9 V u f l = ( 4 / + P L , / ) i u l p z (7) I

p ( k ) = - C P ( j q )

Nwin j=k-( N - I )

where T, is the sample period and NWin is an integer The Two identification algorithms are presented: direct lowpass filter is implemented as follows:

F ( ~ ) = F ( ~ - I ) + ( P ( ~ ) - ~ ( k - ~ w i n ) ) Nwin (18)

q ( k ) = g ( k - l ) + ( q ( k ) - q ( k - N w i n I ) i Nwin

identification by decomposition of the current [5],[6],[7] and

identification by Fourier series [ 101

A Identlfication by Fourier series

A periodic current with a zero dc-value i(t) of any form can

With Nwin = Tr/(2 q ) , ?being the fundamental period, the identification response-time corresponds to half the

fundamental period Inserting the filtered values of p and q

1139

calculated by ( 18) in ( 13) and ( 14), the harmonic components

of the currents are obtained The two methods of

identification are compared in the table below

Identification Direct identification Fourier series

Measured parameters

Harmonics identified

non-linear currents non-linear currents

and phase voltages one component with 5", 7m,

time I T 1 4 5 T I

Response time

Relative calculation

IV CONTROLLER DESIGN

all harmonics ll*and 13*

half hdamental half hdamental period period

approximately

Since the controllers are to be implemented in a micro-

controller, the controllers are designed in the z-plane

A Internal loop

The internal loops need a response time as fast as

possible PI-, PID-, 2nd order pole-placement- and a deadbeat

controllers are analysed and compared in the following A

delay of one sample is introduced in the discrete transfer

functions to carry out control algorithms By z-

transformation, the zero-order-hold equivalent to (7) is:

Sampling frequency& = 5 kHz, inductance Laj = 5 mH and

R4 = 0 I give:

The controllers are tuned to meet a compromise of response-

time, stability and noise rejection To avoid a large

integration of the controllers when the actuator is saturated, a

saturation is implemented in the current-controllers The

responses to a step on the current reference ief simulated

with the circuit on Fig 3 using the four designed current-

controllers are shown in Fig 6

Fig 6 Simulation of the responses to a step on the current reference iaejto the internal loop in the D- and Q-axis Switching- and

sampling frequency 5 kHz

The Fig 7 presents the Bode diagram of the closed loop frequency responses of the internal loops for the four controllers A phase lag appears in all cases, and only the deadbeat controller has a near unity gain at all frequencies

f l H 4

Fig 7 Bode diagram of the closed loop frequency response for 1: PI-, 2: PID-, 3: pole-placement- and 4: deadbeat controller

The analysis of the current controllers shows that the deadbeat controller has the best performance in terms of response to a step on the reference and closed loop frequency response The inconvenient is that it easy saturates the actuator and thereby a decrease of performance The pole placement controller gives the worst result, and the PI and PID controllers are almost equal For the experiment, two controllers will be considered: the deadbeat controller for its excellent performance, and the PI controller for its compromise of simplicity - performance

B External loop

By z-transformation, the zero-order-hold equivalent to the external loop transfer function (4) is:

The system is designed using a sampling frequency& = 5 kHz and a capacitance C, = 0.4 mF With a proportional gain

Kp = 0.06 and an integral gain Ti = 0.01 s, the response to a step on the reference gives a rise-time of 12 ms and an overshoot of 10 YO

1140

V COMPENSATION OF CURRENT CONTROLLER ERROR

Fig 7 shows that the PI current controller introduces a

gain- and phase error in closed loop for the harmonic current

only a phase error

references For the deadbeat controller there is practically

A Compensation for the PI controller

time are used and the switching (and sampling) frequency iS

5 kHz The following circuit parameters are used:

enet, = 327 cos(w,t) ener2 = 327 cos(o,t - 2 4 3 ) 2=T5 - 0 i z

L4 = 5 m H

het =OmH LIOd = I mH

= O I S z

Cd = 400 CIF

enet3 = 327 cos(o/t - 4 n / 3 ) &oaf = 75 iz Cimd = 100 pF

A Simulation by Fourier Method

An optimal implementation frequency of the PI-controller

is f&,=50 Hz At this frequency the gain- and phase errors are

the same for the 5" and 7* harmonic, and the same for the

1 l* and 13& harmonic currents To eliminate these errors, the

harmonic current references are obtained as a modification of

the identified harmonic currents according to Fig 8, with the

gain and phase shift determined from Fig 7, (same for the

1 l* and 13" harmonic) Because the 5* and 1 l* harmonic

appear in the inverse system, they are phase-shifted in the

inverse direction For this method, each harmonic needs to be

known independently from each other, the Fourier

identification is required In the following this method is

referred as the Fourier Method

Fig 8 Harmonic current references are obtained by modification of the

identified harmonic currents in order to compensate the error

introduced by the current PI-controller

B Compensation for the deadbeat controller

It is advantageous to implement the deadbeat controller in

the ap reference frame since it eases the calculation and

removes the cross-coupling terms of (3) The phase error

appears because of the rise-time of two sample periods (see

Fig 6 and 7) The most efficient way to compensate this

error, is to predict the current reference by two sample

periods During stationary conditions this can be done by

using memorised values from the preceding fundamental half

period The current reference to the sample instant k is given

hereafter (23) The error of the current controller is

eliminated under stationary conditions

In the following this method is referred as the Direct Method

VI SIMULATION

The circuit in Fig 3 is simulated using the software

package SUCCESS on a SUN workstation with the

identification and control algorithms already presented The

voltage reference is vd,,=750 V, ideal switches without dead

The 5*, 7*, 1 l* and 13* harmonic currents are identified

by Fourier series PI controllers are used in the internal and external loops The amplitude and phase errors of the individual harmonics from Fig 7 are compensated as showed

in Fig 8 The results are presented in the figure 9

2o i l o a d [ ~ ] No compensation Compensation

50

0

7 6 0 I >\ r , A A n , rr ~

I \ J

I

0 30 0 0 1 0 0 2 0 c 3 0 0 4 0 05

time [SI

inec Hamunic current m %of fundamntal Solution A

Fig 9 Simulation of the ASD - active filter compensating a diode bridge with the Fourier Method The compensation starts at t=0.025 s Below the harmonic content of the network phase current before (black) and after compensation of the 5*, 7*, 1 l* and 13* harmonics

(grey)

B Simulation by Direct Method

The harmonic current component is identified directly by decomposition of the current A PI-controller is used in the external voltage loop, and deadbeat controllers, implemented

in the stationary ap domain, are used in the internal current

loops The current references are predicted by memorisation

(23) The simulation results are presented in the figure 10 The harmonics are not totally compensated This is due to small errors in the compensation of the network voltages (Fig 9, and for the Fourier Method also due to errors in the cross-coupling compensation (Fig 5 ) and errors in the compensation of the error introduced by the current PI- controller (Fig 8)

1141

-

0

7 3 3 7 I I , 1 , / I , , , , I I

time [E]

ha Hanmnic cunent m % of fundsmental Solution B

c 0 0 0 0 1 0 32 0 0 3 3 34 O 05

Fig 10 Simulation of the ASD - active filter compensating a diode

bridge with the Direct Method The compensation starts at t=0.025 s

Below the harmonic content of the network phase current before

(black) and after compensation of the harmonics (grey)

VII EXPERIMENTATION The simulations have been validated on experiments

corresponding to the circuit on Fig 3 with a vario-

transformer between the converter and the network The dc-

link reference voltage vd,/=60 V The circuit parameters are: . .

L$ = 5 m H

LId = 0 mH

vne,, = 20 c o s ( w / t )

vnett = 20 cos(wjt - 2 4 3 ) Rd = 40 R

Rd = 0.1 SZ

40 SZ

= Cd = I100 p F

C i d = I100 CIF

vnet3 = 20 cos(w/t - 4 x / 3 )

The control system is entirely numerical, and consists of a

floating point DSP (ADSP-2 1020) which carries out the

control algorithms, and a 16 bit microcontroller (Intel

80C 196KC 16) which generates the IGBT control signals

The switching and sampling frequencies are 5 kHz The

calculation time of the control algorithms, computed by the

DSP is in a sampling period 82 ps for the Fourier Method

(identification of 5* to 13* harmonics) and 55 ps for the

Direct Method Voltage sensors are necessary for the direct

identification used in the Direct Method

No compensation

4 s

Fig 11: Experimental result Phase currents of the non-linear load, the rectifier - active filter and the network, before and after harmonic compensation of the 5* and 7* harmonics using the Fourier Method

(PI current controller and the Fourier identification) The relative 5"

and 7* harmonic of the network current are much lower with the

compensation

B Experimentation by Direct Method

in& Harmonic cumnt u1 %of fundamental Solution B

20

-

The results (Fig 1 1 - 12) are not as good as those obtained by

simulation, (Fig 9 - 10) There are several reasons for that: Fig 12: Experimental result Phase currents of the non-linear load, the rectifier - active filter and the network, before and after h h o n i c

compensation using the Direct Method: deadbeat controller and the direct identification The relative 5* and 7* harmonic of the network

current are much lower with the compensation

Obviously, the experimentation is not optimized, but it serves

to validate the algorithms, and enables to compare the two For the Fourier Method on Fig 11 the 5th harmonic is

and changes in the non-1inear load currents

causes an error because the harmonic identification is

based on the previous half fundamental period

The switch dead time of 7 ps causes an error

Limited rate of change of phase current, because the

difference between the network- and the dc-link voltage

A Experimentation by Fourier Method

1142

reduced of 60 % and the 7* of 70 %, whereas the higher

harmonics are increased or unchanged For the Direct

Method on Fig 12 the 5* and 7* harmonic network currents

are reduced of 60 %, the rest being unchanged

By simulation, the best result is obtained with the Direct

Method, and the experimental results are almost equal for the

two methods Because the algorithms of the Direct Method

are furthermore faster, this method is chosen as the most

optimal control strategy

VIII LIMIT OF COMPENSATION

The aim is to determine the number of ASDs of equal

motor power rating that can be compensated by the ASD -

active filter With the objective to pass right below the limits

imposed by the standards, it is obvious from the introduction,

that with standards still being uncertain, only a very

approximate result can be given Furthermore the harmonic

content of the diode bridge line currents largely depends on

the line impedance and on the load For an ASD - active filter

which compensates a diode bridge, the maximal phase

current in the ASD - active filter is the s u m of the amplitudes

of the I*, 5* and 7* harmonics (which are approximately in

phase) of the controlled rectifier (other harmonics are

neglected) The current amplitude in the transistors equals

the phase current amplitude:

Thereby, the current rating of the transistors imposes a limit

of harmonic compensation By calculations which are

omitted here, based on means hypothesis, it is found that one

ASD - active filter typically is able to compensate 3 to 5

conventional ASDs of equal motor rating in stationary state

and 1 to 3 ASDs of equal motor power rating in transient

state When the rectifier acts as an active filter, a ripple

appears on the dc-link voltage The following equation is

deduced using elementary calculations, expressing the peak-

peak ripple dc-link voltage as function of the 5" and 7*

harmonic current amplitudes of the rectifier

V, is the dc-link mean voltage, ay the fundamental angular

velocity and Cay I the amplitude of the fundamental rectifier

phase voltage This allows to dimension the converter -

active filter

Ix PERSPECTIVES

-

From an ASD marketing study, it appears that ASDs are very

often sold and installed through a set of several drives

(typically from 2 to 10, and sometimes more) In addition,

the more ASDs are installed, the more the probability of

harmonic pollution risk is high Therefore, the ASD - Active

Filter is well suited to ASD market Furthermore, with a more

general approach, the ASD - Active Filter can filter any no7-

1143

linear load, and not only ASDs It can therefore be a very interesting product to offer to clients requesting ASDs, knowing that all clients are potentially concemed with harmonic pollution, especially in a near future if they have to respect harmonic pollution limits at the connection of the plant to the utility power network

X CONCLUSION

This paper treats the original idea of combining an active filtering capability in a controlled rectifier of the ASD itself Methods of harmonic current identification, current control and elimination of control error are analysed by simulation and experimentation The best solution is to use a deadbeat current controller, direct current identification by decomposition of the current and error compensation by prediction of the current references It is found, that an ASD - active filter in a typical case is able to compensate the harmonics of 5 diode rectifiers of the same power rating in stationary state A relation of 2-3 is obtained in transient state

ACKNOWLEDGMENT

The authors thank Frede BLAABJERG from the University

of Aalborg, Denmark, and Pascal FUOUAL from EDF, France, for their fruitful advices

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- -